To solve the equation \(3a - (10 + 5a) = 54\), we need to simplify and solve for \(a\). Let's go through the steps:

### Step 1: Distribute and Simplify
Expand the expression inside the parentheses and distribute the negative sign:

\[
3a - 10 - 5a = 54
\]

Combine like terms:

\[
(3a - 5a) - 10 = 54
\]

\[
-2a - 10 = 54
\]

### Step 2: Isolate the Variable
Add 10 to both sides to isolate the term with \(a\):

\[
-2a = 54 + 10
\]

\[
-2a = 64
\]

### Step 3: Solve for \(a\)
Divide both sides by -2:

\[
a = \frac{64}{-2}
\]

\[
a = -32
\]

### Solution
The solution is:

\[
\boxed{a = -32}
\]

Would you like more details on any step or have any questions?

Here are 5 related questions for practice:
1. Solve \(4b - (2 + 3b) = 10\).
2. If \(2x - (5 + 4x) = -7\), what is \(x\)?
3. Solve \(5c - (12 - 7c) = 20\).
4. If \(3y - (y + 8) = 0\), find \(y\).
5. Solve for \(z\): \(6z - (15 + 9z) = -3\).

**Tip:** Always distribute negative signs carefully when simplifying equations.

Discover how to solve the linear equation 3a - (10 + 5a) = 54 with a step-by-step guide. This problem explores key algebraic concepts such as the distributive property and solving for variables. Ideal for students in Grades 7-8.

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